How do you find the domain of #f(x)= sqrt(x+6)/(x-5)#?

1 Answer
Apr 21, 2015

For this function to have a value we need to satisfy two conditions:
(a) an expression under the sign of a square root should not be negative, that is #x+6>=0#;
(b) an expression in the denominator should not be equal to #0#, that is #x-5!=0#.

The first condition resolves into
(a) #x >= -6#
The second one resolves into
(b) #x != 5#

Therefore, the domain of #f(x)=sqrt(x+6)/(x-5)# consists of two segments:
#-6 <= x <5# and #x > 5#